Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 972395, 15 pages
doi:10.1155/2009/972395
Research Article

Fixed Points for Multivalued Mappings and the Metric Completeness

S. Dhompongsa and H. Yingtaweesittikul

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 24 December 2008; Accepted 6 May 2009

Academic Editor: Wataru Takahashi

Copyright © 2009 S. Dhompongsa and H. Yingtaweesittikul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces.